Conventional magnetic resonance (MR) pulse sequences include a preparation phase, a waiting phase, and an acquisition phase that are configured to produce signals from which images can be made. The preparation phase determines when a signal can be acquired and determines the properties of the acquired signal. For example, a first pulse sequence may be designed to produce a T1-weighted signal at a first echo time (TE) while a second pulse sequence may be designed to produce a T2-weighted signal at a second TE. However, a lot of preparations and a lot of short waits, especially when compounded over multiple pulse sequences, can add up to a long time to collect a data set. These conventional pulse sequences are typically designed to provide qualitative results where data are acquired with various weightings or contrasts that highlight a particular parameter (e.g., T1 relaxation, T2 relaxation).
A conventional MR acquisition involves numerous repetitions of prepare/wait/acquire pulse sequences. For example, the first pulse sequence may be applied a large number of times to acquire T1 weighted signals for all voxels in a volume of interest (Rol) and then the second pulse sequence may be applied a large number of times to acquire T2 weighted signals for all the voxels in the Rol. Registering (e.g., aligning) the signals from these two acquisitions may be difficult.
When MR images are generated, they may be viewed by a radiologist and/or surgeon who interprets the qualitative images for specific disease signatures. The radiologist may examine multiple image types (e.g., T1-weighted, T2-weighted) acquired in multiple imaging planes to make a diagnosis. The radiologist or other individual examining the qualitative images may need particular skill to be able to assess changes from session to session, from machine to machine, and from machine configuration to machine configuration. Thus, the images are only as good as the image interpreter and all image based (e.g., qualitative) diagnoses end up being subjective.
Seen from a different point of view, conventional MR uses precise preparation time to create precise preparation conditions that facilitate acquiring precise signals from precise locations at precise points in time to make imprecise qualitative data sets. Conventional MR attempts to force the scanned contents (e.g., water, fat) to emit certain signals at certain times and then reconstructs data from these signals. Regardless of these shortcomings, conventional MR has served the clinical community well for many years.
Twieg proposed an approach involving compressed sensing where a model of a signal was used to reduce the total amount of data needed to reconstruct a parameter map and then to reconstruct an image. Similarly, Doneva et al. proposed random under-sampling to achieve compressed sensing. In the Doneva approach, a pixel will represent its true signal evolution plus aliased signal from other pixels. In one embodiment, the aliasing will only appear as added noise at a pixel. The noise will not have structure and will not correlate to the true signal evolution. The Doneva approach facilitates performing a relatively simple process like Orthogonal Matching Pursuit (OMP) to resolve the correct signal to support image reconstruction. OMP assumes the presence of a constrained dictionary of expected signal evolutions. OMP compares a received signal to the dictionary of signals to identify the signal that was most likely to come from a pixel.
Twieg, Parsing local signal evolution directly from a single-shot MRI signal: a new approach for fMRI, Magn Reson Med 2003, November; 50(5):1043-52, describes a single-shot MRI method that performs single-shot parameter assessment by retrieval from signal encoding. The Twieg method abandons the fundamental simplifying assumption used in conventional MRI methods, that the local intrinsic signal does not change its amplitude or phase during signal acquisition, even though these changes may be substantial, especially during longer periods used in single-shot image acquisitions. Twieg recognized that local decay and phase evolution occur and therefore modeled each signal datum as a sample from (k, t) space rather than k-space. Twieg adopted the view that each datum has its own location in a (k, t) space that also reflects another attribute (e.g., relaxation, decay), where t is the elapsed time. While Twieg anticipated improved accuracy and robustness due to the new signal model, intensive reconstruction computations limited Twieg's progress.
Doneva, et al, Compressed sensing reconstruction for magnetic resonance parameter mapping, Magnetic Resonance in Medicine, Volume 64, Issue 4, pages 1114-1120, October 2010, recognizes that different tissues in the human body can be distinguished in MRI by their intrinsic MR parameters including proton density, longitudinal (T1, spin-lattice) relaxation time, and transverse (T2, spin-spin) relaxation time. Doneva applies a learned dictionary to sparsify data and then uses a model based reconstruction for MR parameter mapping. Doneva identifies that “multiple relaxation components in a heterogeneous voxel can be assessed.” However, Doneva uses an imaging based approach that relies on a library whose curves can, in one example, be characterized by equations of the form:SE=1−2e−t/Tx                 where:        SE is a signal evolution,        t is time, and        Tx is a single relaxation parameter.        
In another, more general example, Doneva uses an imaging based approach that relies on a library whose curves can be characterized by:SE=A+Be−t/C                 where A is a constant, B is a constant, t is time, and C is a single relaxation parameter.Doneva pattern matches a received signal evolution to a curve stored in the library.        
The Doneva library is limited to the idealized, single relaxation parameter curves because the preparation is specific and constrained by the fact that Doneva ultimately reconstructs an image from the acquired data. Thus, any variations in t appear to be constant or linear and any variations in a also appear to be constant or linear.
Twieg and Doneva appear to be limited to conventional imaging sequences that highlight only one or a few parameters. To the extent that Twieg or Doneva use any quantitative sequences, these sequences include an excitation and preparation scheme that generates a contrast between different tissues with different properties. However, the preparation fades over time until no more useful information can be acquired unless preparation is repeated. For example, after about 4-5 seconds, tissues subjected to an inversion recovery sequence designed for T1 contrast will have recovered to their equilibrium state and will yield no more signal. This short time limit compromises the ability to perform three dimensional imaging, imaging of moving targets, and so on. Additionally, Twieg and Doneva appear further limited to acquiring information, associated with one relaxation parameter at a time. Twieg and Doneva appear suited to collecting information about T1 relaxation, T2 relaxation, or one fixed combination of T1 and T2, but not both simultaneously. To the extent that Twieg and Doneva could acquire information about T1 and T2, the sensitivity to either would be constant through the acquisition.